On the reduction of the multidimensional stationary Schrödinger equation to a first-order equation and its relation to the pseudoanalytic function theory

DOI10.1088/0305-4470/38/4/006zbMath1092.81015arXivmath/0408172OpenAlexW2019825968MaRDI QIDQ4654932

Publication date: 10 March 2005

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408172

zbMATH Keywords

quaternions generalized Riccati equation reduction of the Schrödinger equation

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20)

Related Items (8)

Geometry of Riccati equations over normed division algebras ⋮ On explicitly solvable Vekua equations and explicit solution of the stationary Schrödinger equation and of the equationdiv(σ∇u)=0 ⋮ On quaternionic analysis for the Schrödinger operator with a particular potential and its relation with the Mathieu functions ⋮ On a three-dimensional Riccati differential equation and its symmetries ⋮ On a factorization of the Schrödinger and Klein-Gordon operators ⋮ On Beltrami fields with nonconstant proportionality factor on the plane ⋮ On a transplant operator and explicit construction of Cauchy-type integral representations for \(p\)-analytic functions ⋮ On the relationship between \(p\)-analytic functions and Schrödinger equation

This page was built for publication: On the reduction of the multidimensional stationary Schrödinger equation to a first-order equation and its relation to the pseudoanalytic function theory